Consider a foreign market where n firms from different countries are compet-
ing in Nash strategies. Let us assume that each firm chooses a strategic variable
xi with i =1, 2, ..., n which delivers the net profit function:
πi = Πi (xi,βi ,si) - F (1)
where βi = kn=1,k6=i h(xk) for some positive, differentiable and increasing func-
tion h(∙), while F is a fixed cost. The second argument represents the spillovers
induced by the choices of the other firms on firm i’s profits. I assume that
Π(xi,βi,si) is quasiconcave in xi with Π11 < 0.8 Since the main focus will be
on free entry equilibria, I assume that spillovers are negative, Π2 < 0. In general
Π12 could be positive, so that we have strategic complementarity, or negative
so that we have strategic substitutability.
Finally, si is the export policy chosen by the government of country i: in our
main application, this is an export subsidy, but we will take in consideration
also other forms of policies which promote exports. I assume that an increase in
the policy raises profits, Π3 > 0, hence I will define si as an export promotion
policy for country i. I will allow Π13 to be positive or negative: only in the first
case, the policy increases marginal profitability. All forms of trade subsidies
under quantity and price competition imply Π13 > 0, but other indirect forms
of export promotion can be characterized by Π13 < 0.
The welfare of country i, W (si), depends positively on the profits of the
domestic firm and negatively on the cost of its policy. In case of export subsi-
dization, the cost of trade policy is the collection of tax revenue, but this may
imply tax distortions or other kinds of costs due to general equilibrium or polit-
ical considerations. Moreover, in case of lobbying activity, the weight given by
the politicians to the costs of the policy may be smaller. Finally, other forms of
export promotion can have different costs for national welfare. Nevertheless, in
line with the literature on strategic trade policy, our focus will be mainly on the
strategic incentive to export promotion, which will be defined as the indirect
marginal benefit of an increase in si on the profit:
SI = ∏2 (xi,βi,Si) dβi
∂si
As long as this is positive, the government of country i has a strategic reason
for promoting exports beyond any direct reason which depends on the first order
impact of policy on welfare.
I will now present a few examples of market structures which are nested in
the general model. As a first example let us consider a market with substitute
goods where the indirect demand for good i is pi = p xi , Pkn=1,k6=i h(xk) with
p1 < 0andp2 < 0 and the cost function, which includes transport costs, is c(xi)
8 In the paper, any subindex refers to derivatives with respect to the corresponding
argument.